RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-22_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 18.5023 0.642165 2 to 25 16.19 8.1454 0.036661 3 to 26 15.65 17.2416 0.561885 4 to 27 15.73 19.9164 0.721473 5 to 28 16.03 10.3131 0.110031 6 to 29 15.80 25.0841 0.907158 7 to 30 15.84 16.1743 0.488489 8 to 31 15.77 20.3591 0.743724 9 to 32 15.77 17.1292 0.554356 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.746365 Tough bday spacings test for dh-ranFile-2015-09-22_14:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 10 43 59 107 99 79 54 25 15 4 5 (O-E)^2/E 0.1 1.1 2.8 0.9 0.0 0.0 0.1 0.8 0.0 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.960, p= 0.271 RESULTS OF GCD FOR dh-ranFile-2015-09-22_14:31 Euclid's algorithm: p-value, steps to gcd: 0.148634 p-value, dist. of gcd's: 0.560322 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-22_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.828 0.275 0.923 0.350 0.212 0.950 0.118 0.851 Bits 8 to 15---> 0.848 0.511 0.768 0.841 0.629 0.470 0.367 0.656 Bits 16 to 23---> 0.892 0.859 0.870 0.199 0.354 0.867 0.148 0.572 Bits 24 to 31---> 0.137 0.490 0.119 0.818 0.504 0.675 0.547 0.458 KS test for the above 32 p values: 0.765 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-22_14:31, p-values for 5 runs: 0.4710, 0.7358, 0.0005, 0.9200, 0.6528 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-22_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 232 211.4 2.004 2.004 r= 29 5051 5134.0 1.342 3.346 r= 30 23110 23103.0 0.002 3.348 r= 31 11607 11551.5 0.266 3.614 chi-square = 3.614 with df = 3; p-value = 0.694 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-22_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 217 211.4 0.147 0.147 r= 30 5053 5134.0 1.278 1.426 r= 31 23145 23103.0 0.076 1.502 r= 32 11585 11551.5 0.097 1.599 chi-square = 1.599 with df = 3; p-value = 0.340 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-22_14:31 b-rank test for bits 1 to 8, p=0.01592 b-rank test for bits 2 to 9, p=0.37391 b-rank test for bits 3 to 10, p=0.20999 b-rank test for bits 4 to 11, p=0.32994 b-rank test for bits 5 to 12, p=0.96576 b-rank test for bits 6 to 13, p=0.93654 b-rank test for bits 7 to 14, p=0.93444 b-rank test for bits 8 to 15, p=0.11739 b-rank test for bits 9 to 16, p=0.45940 b-rank test for bits 10 to 17, p=0.59282 b-rank test for bits 11 to 18, p=0.08514 b-rank test for bits 12 to 19, p=0.70177 b-rank test for bits 13 to 20, p=0.42346 b-rank test for bits 14 to 21, p=0.23785 b-rank test for bits 15 to 22, p=0.04309 b-rank test for bits 16 to 23, p=0.34485 b-rank test for bits 17 to 24, p=0.47460 b-rank test for bits 18 to 25, p=0.83804 b-rank test for bits 19 to 26, p=0.45684 b-rank test for bits 20 to 27, p=0.04950 b-rank test for bits 21 to 28, p=0.78064 b-rank test for bits 22 to 29, p=0.45911 b-rank test for bits 23 to 30, p=0.06348 b-rank test for bits 24 to 31, p=0.93433 b-rank test for bits 25 to 32, p=0.83609 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.548710 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-22_14:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 142092 0.43 0.665237 2 142327 0.98 0.835434 3 141610 -0.70 0.242161 4 142478 1.33 0.908021 5 142297 0.91 0.817471 6 142044 0.31 0.623486 7 142108 0.46 0.678741 8 141709 -0.47 0.319871 9 141601 -0.72 0.235640 10 142422 1.20 0.884508 11 142151 0.56 0.713844 12 141725 -0.43 0.333351 13 141693 -0.51 0.306624 14 142272 0.85 0.801603 15 141924 0.03 0.513671 16 142090 0.42 0.663534 17 141951 0.10 0.538780 18 142641 1.71 0.956322 19 142162 0.59 0.722522 20 141856 -0.12 0.450419 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-22_14:31 Bits used No. missing words z-score p-value 23 to 32 142154 0.8437 0.800579 22 to 31 141531 -1.3046 0.096017 21 to 30 141538 -1.2804 0.100194 20 to 29 142085 0.6058 0.727663 19 to 28 141678 -0.7977 0.212525 18 to 27 142128 0.7540 0.774586 17 to 26 141823 -0.2977 0.382970 16 to 25 142105 0.6747 0.750075 15 to 24 141595 -1.0839 0.139205 14 to 23 141720 -0.6529 0.256923 13 to 22 141715 -0.6701 0.251396 12 to 21 141101 -2.7873 0.002657 11 to 20 141784 -0.4322 0.332808 10 to 19 141780 -0.4460 0.327811 9 to 18 142089 0.6196 0.732224 8 to 17 141949 0.1368 0.554403 7 to 16 141494 -1.4322 0.076047 6 to 15 141486 -1.4598 0.072178 5 to 14 141621 -0.9942 0.160053 4 to 13 141998 0.3058 0.620106 3 to 12 142104 0.6713 0.748978 2 to 11 141791 -0.4080 0.341624 1 to 10 141756 -0.5287 0.298498 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-22_14:31 Bits used No. missing words z-score p-value 28 to 32 142020 0.3752 0.646227 27 to 31 141965 0.1887 0.574841 26 to 30 141825 -0.2859 0.387491 25 to 29 141669 -0.8147 0.207628 24 to 28 141918 0.0294 0.511723 23 to 27 141426 -1.6384 0.050668 22 to 26 142346 1.4802 0.930595 21 to 25 142159 0.8463 0.801318 20 to 24 142108 0.6735 0.749672 19 to 23 141578 -1.1232 0.130686 18 to 22 141995 0.2904 0.614248 17 to 21 141589 -1.0859 0.138770 16 to 20 141409 -1.6960 0.044940 15 to 19 142185 0.9345 0.824970 14 to 18 141886 -0.0791 0.468483 13 to 17 141804 -0.3571 0.360527 12 to 16 141561 -1.1808 0.118845 11 to 15 141326 -1.9774 0.023999 10 to 14 141256 -2.2147 0.013391 9 to 13 141794 -0.3909 0.347917 8 to 12 141927 0.0599 0.523882 7 to 11 141756 -0.5198 0.301615 6 to 10 141957 0.1616 0.564187 5 to 9 141520 -1.3198 0.093457 4 to 8 141797 -0.3808 0.351683 3 to 7 141947 0.1277 0.550805 2 to 6 141921 0.0396 0.515778 1 to 5 142314 1.3718 0.914931 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-22_14:31 Bits used No. missing words z-score p-value 31 to 32 141587 -0.9508 0.170846 30 to 31 142169 0.7660 0.778158 29 to 30 142391 1.4209 0.922321 28 to 29 141808 -0.2989 0.382505 27 to 28 142216 0.9046 0.817170 26 to 27 141625 -0.8387 0.200810 25 to 26 141778 -0.3874 0.349229 24 to 25 140965 -2.7856 0.002671 23 to 24 142246 0.9931 0.839676 22 to 23 142056 0.4327 0.667367 21 to 22 141935 0.0757 0.530180 20 to 21 142123 0.6303 0.735749 19 to 20 141297 -1.8063 0.035437 18 to 19 142242 0.9813 0.836784 17 to 18 141733 -0.5201 0.301480 16 to 17 142212 0.8928 0.814026 15 to 16 142070 0.4740 0.682233 14 to 15 142122 0.6273 0.734784 13 to 14 141584 -0.9597 0.168609 12 to 13 141953 0.1288 0.551250 11 to 12 142182 0.8043 0.789399 10 to 11 142478 1.6775 0.953277 9 to 10 141638 -0.8004 0.211744 8 to 9 142144 0.6922 0.755607 7 to 8 141860 -0.1455 0.442152 6 to 7 141916 0.0197 0.507849 5 to 6 141735 -0.5142 0.303539 4 to 5 141892 -0.0511 0.479615 3 to 4 141464 -1.3137 0.094481 2 to 3 141595 -0.9272 0.176904 1 to 2 141710 -0.5880 0.278268 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-22_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2461.03 -0.551 0.290780 Test results for specific bytes for dh-ranFile-2015-09-22_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2398.31 -1.438 0.075197 2 to 9 2598.87 1.398 0.918980 3 to 10 2493.50 -0.092 0.463407 4 to 11 2478.57 -0.303 0.380927 5 to 12 2560.90 0.861 0.805437 6 to 13 2499.74 -0.004 0.498532 7 to 14 2561.55 0.870 0.807984 8 to 15 2496.03 -0.056 0.477592 9 to 16 2465.03 -0.495 0.310441 10 to 17 2423.26 -1.085 0.138900 11 to 18 2675.49 2.482 0.993463 12 to 19 2557.55 0.814 0.792159 13 to 20 2559.36 0.840 0.799407 14 to 21 2549.67 0.702 0.758791 15 to 22 2535.06 0.496 0.689977 16 to 23 2454.27 -0.647 0.258899 17 to 24 2444.53 -0.784 0.216387 18 to 25 2406.95 -1.316 0.094093 19 to 26 2557.58 0.814 0.792266 20 to 27 2627.39 1.802 0.964198 21 to 28 2426.06 -1.046 0.147857 22 to 29 2347.28 -2.160 0.015396 23 to 30 2474.16 -0.365 0.357388 24 to 31 2560.82 0.860 0.805132 25 to 32 2480.67 -0.273 0.392281 CDPARK for dh-ranFile-2015-09-22_14:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3534 0.5023 0.692266 3513 -0.4566 0.323972 3532 0.4110 0.659449 3496 -1.2329 0.108811 3528 0.2283 0.590298 3523 0.0000 0.500000 3531 0.3653 0.642555 3540 0.7763 0.781201 3501 -1.0046 0.157553 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3520.00 sample std.=14.98 p-value of the KSTEST for those 10 p-values: 0.668283 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-22_14:31 0.7335,0.0861,0.5228,0.1911,0.6417,0.5160,0.0933,0.1090,0.9167,0.0741, The KS test for those 10 p-values: 0.228938 The 3DSPHERES test for dh-ranFile-2015-09-22_14:31 sample no r^3 equiv. uni. 1 12.986 0.351362 2 2.956 0.093845 3 0.429 0.014191 4 64.938 0.885205 5 46.338 0.786600 6 8.110 0.236886 7 23.281 0.539777 8 0.730 0.024044 9 0.727 0.023938 10 7.332 0.216824 11 51.219 0.818644 12 29.902 0.630914 13 106.494 0.971269 14 42.799 0.759882 15 11.001 0.306988 16 7.336 0.216923 17 6.499 0.194786 18 73.400 0.913420 19 167.482 0.996238 20 56.131 0.846036 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.296576 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-22_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 -0.8 -0.8 -0.4 -0.5 -0.8 1.2 0.6 1.9 -1.3 0.3 -1.1 -0.7 -0.7 1.6 -0.3 0.1 1.5 -0.1 -1.9 0.2 0.7 -0.8 0.1 1.4 -0.2 0.4 0.8 -1.1 -1.2 -0.8 -0.0 -0.8 0.5 -1.2 -0.7 0.8 -0.8 1.0 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:35.732233 z-score=-0.683869, p-value=0.258676 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-22_14:31 Test no p-value 1 0.802617 2 0.065400 3 0.067377 4 0.834844 5 0.750420 6 0.040375 7 0.017439 8 0.057367 9 0.342918 10 0.049869 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003290 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-22_14:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66850 0.50 66446 0.73 3 25000.00 24841 1.01 25080 0.26 4 6666.67 6666 0.00 6761 1.33 5 1388.89 1381 0.04 1411 0.35 6 238.10 224 0.83 258 1.66 7 34.72 33 0.09 39 0.53 8 4.96 4 0.19 4 0.19 p=0.15052 p=0.46266 Number of rngs required: 688723, p-value: 0.644 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-22_14:31 No. of wins: Observed Expected 98684 98585.9 z-score= 0.439, pvalue=0.66965 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66754 66666.7 0.114 0.114 2 37719 37654.3 0.111 0.226 3 26922 26954.7 0.040 0.265 4 19396 19313.5 0.353 0.618 5 13810 13851.4 0.124 0.742 6 9836 9943.5 1.163 1.905 7 7093 7145.0 0.379 2.284 8 5053 5139.1 1.442 3.725 9 3734 3699.9 0.315 4.040 10 2676 2666.3 0.035 4.076 11 1928 1923.3 0.011 4.087 12 1378 1388.7 0.083 4.170 13 1046 1003.7 1.781 5.951 14 746 726.1 0.543 6.495 15 501 525.8 1.173 7.668 16 378 381.2 0.026 7.694 17 308 276.5 3.579 11.273 18 187 200.8 0.952 12.225 19 139 146.0 0.334 12.559 20 102 106.2 0.167 12.727 21 294 287.1 0.165 12.892 Chisq= 12.89 for 20 degrees of freedom, p= 0.11802 SUMMARY of craptest p-value for no. of wins: 0.669650 p-value for throws/game: 0.118018 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-22_14:31 No. of wins: Observed Expected 98965 98585.9 z-score= 1.696, pvalue=0.95503 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67092 66666.7 2.714 2.714 2 37614 37654.3 0.043 2.757 3 26721 26954.7 2.027 4.784 4 19295 19313.5 0.018 4.801 5 13709 13851.4 1.464 6.266 6 9923 9943.5 0.042 6.308 7 7122 7145.0 0.074 6.382 8 5135 5139.1 0.003 6.385 9 3721 3699.9 0.121 6.506 10 2635 2666.3 0.367 6.874 11 1891 1923.3 0.543 7.417 12 1405 1388.7 0.190 7.607 13 1035 1003.7 0.975 8.582 14 738 726.1 0.194 8.776 15 574 525.8 4.412 13.188 16 376 381.2 0.070 13.257 17 269 276.5 0.206 13.463 18 196 200.8 0.116 13.579 19 159 146.0 1.160 14.740 20 105 106.2 0.014 14.753 21 285 287.1 0.016 14.769 Chisq= 14.77 for 20 degrees of freedom, p= 0.21053 SUMMARY of craptest p-value for no. of wins: 0.955033 p-value for throws/game: 0.210530 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0027,0.0027,0.0033,0.0134,0.0142,0.0154,0.0159,0.0174,0.0239, 0.0240,0.0240,0.0354,0.0367,0.0404,0.0431,0.0449,0.0495,0.0499,0.0507, 0.0574,0.0635,0.0654,0.0674,0.0722,0.0741,0.0752,0.0760,0.0851,0.0861, 0.0933,0.0935,0.0938,0.0941,0.0945,0.0960,0.1002,0.1088,0.1090,0.1100, 0.1174,0.1180,0.1181,0.1188,0.1193,0.1307,0.1368,0.1388,0.1389,0.1392, 0.1479,0.1483,0.1486,0.1505,0.1576,0.1601,0.1686,0.1688,0.1708,0.1769, 0.1911,0.1948,0.1990,0.2008,0.2076,0.2100,0.2105,0.2117,0.2125,0.2125, 0.2164,0.2168,0.2169,0.2289,0.2356,0.2369,0.2378,0.2422,0.2514,0.2569, 0.2587,0.2589,0.2708,0.2751,0.2783,0.2908,0.2966,0.2985,0.3015,0.3016, 0.3035,0.3066,0.3070,0.3104,0.3199,0.3240,0.3278,0.3299,0.3328,0.3334, 0.3404,0.3416,0.3429,0.3448,0.3479,0.3492,0.3501,0.3514,0.3517,0.3543, 0.3574,0.3605,0.3671,0.3739,0.3809,0.3825,0.3830,0.3875,0.3923,0.4235, 0.4422,0.4504,0.4568,0.4582,0.4591,0.4594,0.4627,0.4634,0.4685,0.4700, 0.4710,0.4746,0.4776,0.4796,0.4885,0.4900,0.4985,0.5000,0.5037,0.5078, 0.5105,0.5117,0.5137,0.5158,0.5160,0.5228,0.5239,0.5302,0.5388,0.5398, 0.5467,0.5487,0.5508,0.5513,0.5544,0.5544,0.5603,0.5619,0.5642,0.5716, 0.5748,0.5903,0.5928,0.6142,0.6201,0.6235,0.6286,0.6309,0.6417,0.6422, 0.6426,0.6437,0.6462,0.6528,0.6558,0.6594,0.6635,0.6652,0.6674,0.6683, 0.6696,0.6754,0.6787,0.6822,0.6900,0.6923,0.6938,0.7018,0.7138,0.7215, 0.7225,0.7277,0.7322,0.7335,0.7348,0.7357,0.7358,0.7437,0.7464,0.7490, 0.7497,0.7501,0.7504,0.7556,0.7588,0.7599,0.7655,0.7684,0.7746,0.7782, 0.7806,0.7812,0.7866,0.7894,0.7922,0.7923,0.7994,0.8006,0.8013,0.8016, 0.8026,0.8051,0.8054,0.8080,0.8140,0.8172,0.8175,0.8185,0.8186,0.8250, 0.8282,0.8348,0.8354,0.8361,0.8368,0.8380,0.8397,0.8412,0.8460,0.8483, 0.8506,0.8595,0.8667,0.8702,0.8845,0.8852,0.8919,0.9072,0.9080,0.9134, 0.9149,0.9167,0.9190,0.9200,0.9223,0.9227,0.9306,0.9343,0.9344,0.9365, 0.9501,0.9533,0.9550,0.9563,0.9642,0.9658,0.9713,0.9935,0.9962, Overall p-value after applying KStest on 269 p-values = 0.177620 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.